Hermitian Metric
A
hermitian metric
on a
complex vector bundle
E
over a
smooth manifold
M
, is a
positive-definite
,
hermitian
inner product
on each
fiber
E
p
, that varies smoothly with the point
p
in
M
. An important special case is that of a hermitian metric on the
complexified
tangent bundle
TM \otimes \mathbb C
of a
complex manifold
M
. This is the hermitian analogue of a
Riemannian metric
. Every complex manifold admits such a hermitian metric.
See also
:
Khler metric
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